Table Of ContentHydrodynamic Instability and Transition
to Turbulence
FLUID MECHANICSAND ITSAPPLICATIONS
Volume100
SeriesEditors: RenéMOREAU
EcoleNationaleSupérieured’HydrauliquedeGrenoble
BoîtePostale95
38402SaintMartind’HèresCedex,Franceh
AndreTHESS
DepartmentonMechanicalEngineering
IlmenauUniversityofTechnology
98684Ilmenau,Germany
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Thepurposeofthisseriesistofocusonsubjectsinwhichfluidmechanicsplaysa
fundamentalrole.
Aswellasthemoretraditionalapplicationsofaeronautics,hydraulics,heatandmass
transfer etc., books will be published dealing with topics which are currently in a
stateofrapiddevelopment, suchasturbulence, suspensionsandmultiphasefluids,
superandhypersonicflowsandnumericalmodelingtechniques.
Itisawidelyheldviewthatitistheinterdisciplinarysubjectsthatwillreceiveintense
scientific attention, bringing them to the forefront of technological advancement.
Fluidshavetheabilitytotransportmatteranditspropertiesaswellastotransmitforce,
thereforefluidmechanicsisasubjectthatisparticularlyopentocrossfertilization
withothersciencesanddisciplinesofengineering. Thesubjectoffluidmechanics
will be highly relevant in domains such as chemical, metallurgical, biological and
ecologicalengineering.Thisseriesisparticularlyopentosuchnewmultidisciplinary
domains.
The median level of presentation is the first year graduate student. Some texts are
monographsdefiningthecurrentstateofafield; othersareaccessibletofinalyear
undergraduates;butessentiallytheemphasisisonreadabilityandclarity.
Forfurthervolumes:
http//:www.springer.com/series/5980
Akiva M.Yaglom† (cid:129) Uriel Frisch
Author Editor
Hydrodynamic Instability and
Transition to Turbulence
2123
Author Editor
AkivaM.Yaglom† UrielFrisch
ObservatoiredelaCôted’Azur
UNS,CNRS,LaboratoireLagrange,OCA
Nice,France
Everyefforthasbeenmadetocontactthecopyrightholdersofthefigureswhichhavebeen
reproducedfromothersources.Anyonewithacopyrightclaimwhohasnotbeenproperly
creditedisrequestedtocontactthepublishers,sothatdueacknowledgementsmaybemade
insubsequenteditions.
ISSN0926-5112
ISBN978-94-007-4236-9 ISBN978-94-007-4237-6(eBook)
DOI10.1007/978-94-007-4237-6
SpringerDordrechtHeidelbergLondonNewYork
LibraryofCongressControlNumber:2012951398
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Foreword
AkivaMoiseevichYaglom(1921–2007)wasamajorfigureofturbulenceresearch,
closelyassociatedwiththegiantscientistAndreiNikolaevichKolmogorov.Formore
biographicalinformationonA.M.Yaglom, seetheobituarybyPeterBradshaw(in
Flow, Turbulence and Combustion, vol. 80 (3), 287–289, April 2008), a copy of
whichfollowsthisForeword.
Together withAndrei Monin,A.M.Yaglom was the author of “Statistical Fluid
Mechanics:MechanicsofTurbulence”(MITPressvol.11971,vol.21975,repub-
lishedbyDoverPublications,2007).WitheditinghelpfromJohnL.Lumley,thiswas
a much augmented and revised English edition of the Russian originals published
in1965(vol. 1)and1967(vol. 2)byNaukaPress, Moscow.Thesebooks, usually
known as MY1 and MY2, by far the most detailed account of the subject (close
to 2000 pages), had become the standard references in turbulence research when
YaglomemigratedtotheUSAin1992.Stillveryactive,hesetouttoreviseMonin
andYaglom’sbook,startingwiththoseaspectsofvol.1dealingwith“Hydrodynamic
Instabilities and Transition to Turbulence,” a subject which had grown very much
since1971andwhichhewasfollowingclosely.Afterabouttenyearsofwork,four
monographs totalling more than 800 pages were produced in preliminary form by
the Center forTurbulence Research (CTR, Stanford University) with considerable
editing help from Peter Bradshaw. This material (CTR Chap. 2–5) covered only
about one quarter of the topics of MY1 but in a coherent and self-consistent way
suitableforastandalonepublicationratherthananeweditionofMY1.In2004,at
the10thEuropeanTurbulenceConference(Trondheim)Yaglomdiscussedthematter
withthepublisherSpringerandthisishowtheprojectofthepresentbookwasborn.
Duringthenextthreeyears,A.M.Yaglompreparedanintroductorychapter(Chap.1
of the present book) and worked on two additional chapters which unfortunately
could not be completed before his death. The present book thus contains an intro-
ductorychapterandtheCTRChap.(2–5)entitled,respectively,“Basicexperimental
factsandintroductiontolinearstabilitytheory”,“Moreaboutlinearstabilitytheory;
studiesoftheinitial-valueproblem”,“Stabilitytofinitedisturbances:energymethod
andLandau’sequation”and“Furtherweakly-nonlinearapproachestolaminar-flow
stability:Blasiusboundarylayerflowasaparadigm”.
v
vi Foreword
Publication of the present book has been further delayed because the original
files of the CTR monographs and of the figures could not be located. Fortunately
manypeoplehelpedinrestoringthematerial.ThanksarethusduetoPeterBradshaw,
JuliaYaglom,Yuni Rodman-Yaglom, Naomi Sherman,Victor Privalsky and many
others.ThanksarealsoduetoSpringerVerlagandparticularlytoNathalieJacobs,
AnnekePotandCrestPremediaSolutions,Pune.Eachchapterendswiththeauthor’s
ownacknowledgmentsinwhichheexpresseshisgratitudetothosewhohelpedhim
scientificallyorotherwise.
UrielFrisch,Nice
In memory of Akiva M. Yaglom
AkivaMoiseevichYaglomdiedinBoston,MAon13December2007,afterashort
illness.AkivaandhisbrotherIsaakwerebornon6March1921(correctdate:thereare
otherversions)inKharkov,Ukraina(thenpartoftheSovietUnion).Theyweresaid
tobeasalikeastwodropsofwater.Isaakwasalsoadistinguishedmathematician,
andthebrotherswroteseveralbookstogether.ThefamilymovedtoMoscowin1925.
Isaakdiedin1986,andAkivasaidthatonlyatwincouldunderstandwhatitwaslike
toloseatwin.PerhapsthefirstofAkiva’smanyhonorswasaprizeintheMoscow
Mathematical Olympiads, a competition for high school students, in 1938. Akiva
sharedthisprizewithhisbrotherIsaak.TheprizewaspresentedtohimbyAndrei
N.Kolmogorov,oneoftheorganizersofthecompetition.Kolmogorovremembered
himwhentheymetin1941,andinspring1943invitedAkivatodograduatework
withhiminMoscow.Kolmogorov’sinterestinencouragingyoungmathematicians
led,inrathersimilarcircumstances,tohisacquisitionofAleksandrM.Obukhovasa
graduatestudent:thethirdofthesefamousmeteorologists,AndreiS.Moninentered
Kolmogorovsgroupbyamoreconventionalroute.
Thepresentwriterdoesnotknowiftheseappliedstatisticianseverdiscussedthe
probability that their given names should all begin with the same letter. In 1994,
Akiva contributed a detailed and affectionate review A.N. Kolmogorov as a fluid
mechanician and founder of a school in turbulence research to vol. 26 ofAnnual
ReviewsofFluidMechanics.Someofthematerialinthepresentobituarycomesfrom
thatreview. ItsfrontispieceshowsYaglomandKolmogorov, flankedbyKraichnan
and Millionshchikov, at a 1961 conference in Marseille. Yaglom’s undergraduate
studies at Moscow University were interrupted by the Great PatrioticWar (World
War II) and in theAutumn of 1941, when the invasion was nearing Moscow and
many of its citizens were moved to safer locations, he transferred to Sverdlovsk,
about1300kmEastofMoscow,whereMoscowUniversitywasevacuated.Hehad
previouslyvolunteeredformilitaryservicebutwasrejectedbecauseofpooreyesight:
hesaidthatmostofhisfriendswhojoinedupwerekilledandthathisrejectionwas
probablygreatgoodluckforhim. LikehisfortuitousdiscoverybyKolmogorov, it
wascertainlygreatgoodluckforFluidMechanics.
Yaglomremainedinterestedinfundamentalphysicswhileworkingonturbulence.
Afterhefinishedgraduatestudy,I.E.TammandV.L.Ginsburgofferedhimapostat
vii
viii InmemoryofAkivaM.Yaglom
theLebedevPhysicsInstituteoftheRussianAcademyofSciences,Hewasinformed
that part of his work would be connected to the atomic bomb project. That offer
providedanexceptionalopportunitytopursuehisinterestinfundamentalphysics,but
hedeclineditsincehedislikedtheideaofdevelopingabombforStalin.Hetherefore
took a post at the Institute of Theoretical Geophysics of the RussianAcademy of
Sciences (now theA.M. Obukhov Institute ofAtmospheric Physics). He intended
toreturntotheoreticalphysicsassoonashecoulddosowithoutbeinginvolvedin
thefissionbombproject.However,workingintheoreticalphysicswhileremaining
uninvolvedinmilitaryprojectsneverbecamepossibleinSovietRussia,andYaglom
remainedattheInstitute(athirdpieceofgreatgoodluckforFluidMechanics).He
alsorosetoFullProfessoratMoscowUniversity.HeandhiswifeJuneemigratedto
theUnitedStatesin1992,whenhewas70yearsoldbutstillworkingenthusiastically
onscientificproblems.HehadkeptupcontactsintheWest,bothpersonalandpostal,
and the present writer knew him as a valuable pen friend for many years before
meetinghim.
At the suggestion of his friend the late Marten Landahl of the Department of
AeronauticsandAstronauticsatM.I.T.,AkivasettledtherewiththetitleofResearch
Fellow,andcontinuedscientificwork.Untilthelast,heworked10–12hoursaday,
goingtohisMITofficealmosteverydayandspendinglonghoursinhishomeoffice.
His work was supported by the Stanford/NASA Center for Turbulence Research
(CTR), to which he made several working visits, and later by the Poduska Family
Foundation. He also did some consulting work in the Boston area. He travelled
extensivelytoconferencesandotherevents,includingseveralvisitstoRussia.
Yaglomwastheauthororco-authorofsixbooksand120scientificpapers,byno
meansallonturbulence.Oneofthebookswrittenincollaborationwithhisbrother
wastranslatedintoEnglishasInformationTheory,andwasveryrecentlydescribedas
theprincipalRussiantext[onthissubject].Another,multi-volume,bookbythetwins
wasChallengingMathematicalProblemswithElementarySolutions(latestedition
2007)basedpartlyonproblemspreparedfortheMoscowMathematicalOlympiads
whichcontinuetothisday.
Right up to the time of his death, he was working on the revision of Statistical
Hydromechanics, universally known as Monin &Yaglom and covering instability
and transition as well as turbulence. His work on the Instability volume is being
assembled for publication. Monin died on 22 Sept. 2007, less than three months
before his junior author, but he had been inactive for some years.Akiva’s honors,
aswellastheabove-mentionedhigh-schoolprizewhichreallyfoundedhiscareer,
includedthedegreeofDoctorofScience(awardedinRussiaforacorpusofwork
ratherthanasinglethesis),theOttoLaporteAwardoftheAmericanPhysicalSociety
(1988) and the Lewis Fry Richardson Medal of the European Geosciences Union
(2008).TheawardwasannouncedbeforeAkivadied:hiswidowJunewasinvitedto
acceptthemedalforhiminViennainApril.
Richardson’sclassicbook“WeatherPredictionbyNumericalProcess”waspub-
lishedjustoneyearafterYaglomwasborn.Now,atthetimeofhisdeath,thereare
planstobuildacomputerdedicatedtorealizingRichardson’sdreamnumericalso-
lutionsforthewholeofEarth’satmosphere,butwithrathermorecomputingpower
InmemoryofAkivaM.Yaglom ix
thanRichardson’shumorousconceptofamyriad(nominally10,000)humanoper-
atorsofmechanicalcalculatingmachines. LikeKolmogorov,AkivaYaglomtooka
greatinterestinschool-leveleducation,andinhislateryearshesupportedShalom
House in Brighton, MA, which is a school dedicated to combining orthodox Jew-
isheducationwithhigh-gradecoursesinmathematicsandscience.Bookswerehis
life-longpassion,andhecollectedauniquelibraryofseveralthousandvolumes.
LetDebraSpinks,AdministrativeManagerofCTRatthetimeofAkiva’svisits
toStanford,havethelastword:Irememberbestthathewasafascinating,gentlesoul.
PeterBradshaw,StanfordUniversity
Contents
1 TheEquationsofFluidDynamicsandSomeofTheirConsequences 1
1.1 PrincipalEquationsofFluidMechanics ........................ 1
1.2 SomeExamplesofExactandApproximateSolutions
oftheEquations............................................ 10
References..................................................... 25
2 BasicExperimentalFactsandIntroductiontoLinearStabilityTheory 29
2.1 ConceptofTurbulence;TransitiontoTurbulenceinTubes,
Channels,andBoundaryLayers .............................. 29
2.2 FlowPastSolidBodies;Boundary-LayerSeparation
theDragCrisisandtheDependenceofRe onIntensity
cr
andLengthScaleofAvailableDisturbances..................... 40
2.3 HydrodynamicInstability.................................... 45
2.4 SimpleExamplesofUnconditionallyUnstableFluidFlows ....... 48
2.5 LinearStabilityTheoryandMethodofNormalModes............ 51
2.6 LinearStabilityAnalysisofFlowBetweenTwoRotating
Cylinders ................................................. 59
2.7 LinearStabilityAnalysisforaLayerofFluidHeated
fromBelow................................................ 76
2.8 IntroductiontotheLinearStabilityTheoryofParallel
FluidFlows................................................ 86
2.9 ApplicationsofNormal-ModeStabilityAnalysistoSpecific
ParallelandNearlyParallelFlows............................. 116
References..................................................... 154
3 MoreAbout Linear StabilityTheory: Studies of the Initial-Value
Problem ...................................................... 175
3.1 BeginningoftheStory:TheWorksofKelvinandOrr ............ 175
3.2 StudiesoftheInviscidInitial-ValueProblemforDisturbances
inPlane-ParallelFlows ...................................... 181
3.3 TheInitial-ValueProblemforViscousParallelFlows............. 217
xi
